How Do Household Portfolio Shares Vary With Age?

[Pages:87]How Do Household Portfolio Shares Vary With Age?

John Ameriks and

Stephen P. Zeldes

This draft: September 2004

Comments welcome.

Abstract

Using pooled cross-sectional data from the Surveys of Consumer Finances, and new panel data from TIAA-CREF, we examine the empirical relationship between age and portfolio choice, focusing on the observed relationship between age and the fraction of wealth held in the stock market. We illustrate and discuss the importance of the well-known identification problem that prevents unrestricted estimation of age, time and cohort effects in longitudinal data. We also document three important features of household portfolio behavior: significant non-stockownership, wide-ranging heterogeneity in allocation choices, and the infrequency of active portfolio allocation changes (almost half of the sample members made no active changes to their portfolio allocations over our nine-year sample period). When estimating portfolio share equations, we consider three separate exclusion restrictions: excluding time effects, cohort effects, and finally age effects. We find no evidence supporting a gradual reduction in portfolio shares with age. There is some tendency for older individuals to shift completely out of the stock market around the time of annuitizations and withdrawals.

The Vanguard Group. E-mail to: john ameriks@ Graduate School of Business, Columbia University; and NBER. E-mail to: stephen.zeldes@columbia.edu. We are grateful to Joel Dickson, Sarah Holden, Andrew Metrick, Martha Starr-McCluer, Todd Sinai, Mark Warshawsky, and seminar participants at Carnegie-Mellon University, Columbia University, the Federal Reserve Board, New York University, and the University of Chicago for helpful comments and suggestions. This work was performed while Ameriks was a research fellow at the TIAA-CREF Institute; we gratefully acknowledge the assistance of TIAA-CREF staff members in assembling data. Zeldes is grateful for financial support from Columbia Business School. Any errors are the sole responsibility of the authors. All opinions expressed in this document are those of the authors alone.

1 Introduction

How households allocate their financial portfolios has been an increasingly important issue to economists and policymakers alike. There has been a rapid increase in the fraction of U.S. households owning equities, from 33 percent in 1989 to 51 percent in 2001. Much of this has been due to the dramatic growth in individually-directed defined-contribution retirement plans, in which individuals choose how much of their retirement funds are allocated to different assets. Similar patterns of increased equity ownership and added individual control over retirement asset allocation have occurred in many nations around the world, suggesting that the quality of investment decisions made by households will be of increasing importance to their future living standards. As policymakers in the U.S. and elsewhere consider adding an individual-account component to social security systems, a key issue that arises is whether households will make appropriate investment allocation decisions. Poor choices could potentially leave households with unacceptably low retirement consumption.

One important aspect of the financial decisions made by households is how their portfolio allocation changes with age or horizon. Professional financial planners often advise that the fraction of wealth that people should hold in the stock market should decline with age. A typical rule of thumb is that the percentage of an investor's portfolio of financial assets that is held in equities should equal 100 minus her age, so that a 30-year-old would hold 70 percent of her financial wealth in stocks, while a 70-year-old would hold 30 percent in stocks.

The proliferation of this type of advice in the popular press has stimulated increased interest among academic economists in at least two questions regarding these professional prescriptions. First: Should individuals follow this advice and decrease investment in the stock market as they get older? And second: Do individuals follow this advice and actually decrease investment in the stock market as they get older? The goal of this paper is to contribute to the research on these two questions through a careful analysis of how household portfolio choices, and particularly investments in the stock market, actually vary with investor age. The results also have implications, for example, for understanding the effects of stock prices of the aging of the baby boom generation (Bakshi and Chen (1994)).

This is not a simple exercise for a variety of reasons. First, even with perfect data, it is difficult to disentangle empirically the effects that age has on portfolio shares (age effects) from effects related to a person's date of birth (cohort effects) or effects related to the date of observation (time effects). Second, the available data on household asset allocation are not perfect; the data are typically incomplete and may be subject to measurement error. Third, a majority of U.S. households do not hold any wealth in the stock market, either directly or

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indirectly through mutual funds or retirement-savings accounts (such as 401(k)s or IRAs). This suggests the need to model and examine at least two choices: the decision to own stock or not, and (conditional on an affirmative answer) the choice of how much stock to hold.

We use data from two sources in our analysis. The first is pooled, cross-sectional data from the 1962 Survey of Financial Characteristics of Consumers, and the 1983, 1989, 1992, 1995, and 1998 Surveys of Consumer Finances. These data have several desirable attributes. They contain detailed information on a wide variety of assets and liabilities owned by the sampled households and are carefully constructed and weighted so as to be representative of the entire population of U.S. households at the time of each survey. The 1989 through 1998 surveys have very similar formats, enabling relatively easy and legitimate comparisons of the survey results over time.

Our second data source is a unique panel data set constructed at TIAA-CREF (Teachers Insurance and Annuity Association-College Retirement Equities Fund). This data set tracks the quarterly account balances and contributions over a thirteen-year period (19871999) for approximately 16,000 randomly selected TIAA-CREF participants. This is the one of only a few data sets that we know of that tracks portfolio data for the same individuals over many years. It has the added advantage of containing actual account data rather than self-reported data, reducing measurement error dramatically.

The paper is structured as follows. In Section 2, we examine the advice provided by both economic theory and financial industry professionals regarding how portfolio shares should vary with age. We also examine the past empirical evidence on what households actually do. Section 3 describes the modeling and identification issues that must be addressed when performing the empirical work. Section 4 describes the data sets in more detail, and Section 5 presents the results of our analysis of the data. Section 6 concludes.

2 Economic theory, professional prescriptions, and previous evidence

There is a large and growing theoretical literature that addresses whether professional portfolio allocation advice regarding age and equity allocations is appropriate.1 We begin by reviewing the economic theory and the professional prescriptions.

1See Jagannathan and Kocherlakota (1996) for an excellent review of the economic theory of age/horizon effects. Although they are not concerned with the age question, Canner, Mankiw, and Weil (1997) compare professional portfolio advice with the predictions of economic theory.

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2.1 Economic theory

2.1.1 A benchmark model

In the late 1960s, economic theoreticians working on individual financial asset allocation decisions over time ("lifetime asset allocation") showed conditions under which optimal portfolio shares would constant over the life cycle, i.e., independent of both age and wealth (Mossin 1968, Samuelson 1969, Merton 1969). This result is based on several assumptions, the most important of which are: (1) asset returns are independently and identically distributed over time, (2) agents have utility functions of the CRRA class that are time-invariant and additively separable over time, (3) agents have no labor income or nontradeable assets, and (4) markets are frictionless and complete. This is a useful benchmark because it forces us to recognize that one or more of these assumptions must be relaxed to generate optimal portfolio shares that vary with age.

In the subsequent subsections, we relax these assumptions. We note that once we do so, changes in age, as well as changes in variables that themselves change with age, can affect portfolio decisions.2 For example, if utility is not CRRA, wealth may affect portfolio choices, and, because wealth may change in a pattern related to age, age may have an indirect effect on portfolio decisions. As we review the theoretical literature, it is important to be clear whether the age effect being examined is the partial derivative of the asset demand function with respect to age or the total derivative. In the benchmark model, both derivatives are zero. Once we depart from this framework, the two derivatives are no longer necessarily zero, nor are they necessarily the same.

2.1.2 Adding human capital and non-traded assets

If labor income is included in the portfolio choice model, it can cause individuals to optimally change their allocation of financial assets in a pattern related to the life-cycle. Consider first a class of models very close to the perfect markets model described above: assume that labor income is not directly traded, but that there exists a set of traded assets with payouts that are perfectly correlated with labor income (i.e., there is spanning, so that labor income is effectively traded).

As a simple example, assume that labor income is certain, and that perfect markets exist for borrowing and lending. Assume also that there are only two financial assets: a riskfree asset and a risky asset (stocks). Define financial wealth (F Wt) as the sum of the dollar

2In many of the examples below, the relevant variable is the investment horizon rather than age per se. These variables are generally (but not always) closely related, and we do not attempt to distinguish between them in what follows.

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amounts in the these two financial assets, and human wealth (HWt) as the present value of future labor income (i.e., human wealth is not included in measured financial wealth). Finally, define total wealth (T Wt) as financial wealth plus human wealth, and St as the amount of financial wealth held as stocks. Under these assumptions, the optimal allocation of total wealth between the risky and risk-free assets is constant over the lifetime, but the allocation of financial wealth is not: households will alter their holdings of the risk-free financial asset in order to maintain constant overall portfolio weights on risky and risk-free assets, i.e., St/T Wt = St+1/T Wt+1. Households will tend to hold proportionately less of the risk-free financial asset, perhaps even selling short, when young (when the value of certain future labor income is very large), and tend to increase the proportion of financial wealth held in the risk-free financial asset as they age (as the value of future labor income declines).3 While the goal of this activity is to ensure that the share of risky assets in the overall portfolio remains constant, the share of risky assets in the portfolio of financial assets tends to decline with age, up until the point at which there is no future labor income.4

Next consider the situation in which labor income is risky, but perfectly correlated with the payoffs of some portfolio of risky assets. As before, assume that human wealth is measured separately from financial wealth. A simple example of this scenario would be if labor income were perfectly correlated with the payoffs from holding the aggregate stock market.5

In this situation, households will keep constant the fraction of total wealth held in the risk-free asset (and thus the fraction of total wealth held in the sum of the risky asset and human wealth). But because the value of human wealth declines with age, the share of risky assets in the portfolio of financial assets tends to rise with age up until the point at which there is no future labor income.

Consider next the situation when labor income is not spanned by the payoffs on

3If there are borrowing constraints, then individuals desiring to borrow at the risk-free rate in order to invest more in risky assets while young may be prevented from doing so. If the borrowing constraint is not binding later in life, then an obvious life-cycle pattern in asset allocation may emerge.

4As Jagannathan and Kocherlakota (1996) point out, because the total value of financial assets is a random variable, such "increasing conservatism" is not inevitable. In fact, in periods in which there is a decline in the value of financial assets, it is possible that households may increase the percentage of financial portfolios held in stocks. To see this, note that holding overall asset shares constant, i.e., St/T Wt = St+1/T Wt+1 implies St+1/F Wt+1 = (St/F Wt) ? [1 + (HWt+1/F Wt+1)]/[1 + (HWt/F Wt)].

This means that the fraction of financial wealth held in stocks decreases whenever the ratio of human wealth to financial wealth decreases. This will generally occur as age increases, as human wealth decreases and financial wealth tends to increase with age. However, if in a given period, financial wealth happens to fall by a greater percentage than human wealth, the fraction of financial wealth optimally held in stocks will increase.

5With finite-lived individuals, it is not easy (and may not be possible) to construct a general equilibrium model in which this is true.

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